Research on stem taper equation of Scots pine based on generalized additive model

  Objective  Based on the theory of generalized additive model, stem taper equation was constructed for Scots pine (Pinus sylvestris). Accurate variable exponent taper equations such as Zeng et al. (1997), Bi (2000) and Kozak (2004) in forestry were used for comparison.

  Method  The generalized additive taper equation was constructed using DBH, tree height, the height at different stem parts, the diameter at different tree heights and their transformation based on taper data of Scots pine. The model was fitted using the gamm function in mgcv library of the R software. Six smooth splines were chosen for fitting process, i.e. B-spline function (BS), cubic regression spline function (CR), Duchon spline function (DS), Gaussian process smooth spline function (GP), P-spline function (PS) and thin plate regression spline function (TP). The models were validated using leave-one-out cross-validation method.

  Result  (1) The optimal generalized additive model form of taper equation was constructed by response variable relative diameter and explanation variable square of DBH, total height and the square root of relative height. (2) The fitting results showed that the generalized additive taper equations were similar and better than parametric taper equation except for CR function. (3) The cross validation results showed that the generalized additive models (BS, DS, GP, PS and TP) were basically consistent with the fitting results except for CR, i.e. they were superior to parametric taper equation of Zeng et al. (1997), Bi (2000) and Kozak (2004). The BS model had the highest prediction accuracy in the generalized additive models. Kozak (2004) had the highest prediction accuracy in the variable exponential taper equations. (4) Through the simulation of stem curves of BS and Kozak (2004) models, it was found that Kozak (2004) had a large error in predicting the upper part of the stem of a small tree. However, BS had higher accuracy in simulating small tree and large tree.

  Conclusion  The generalized additive model is a nonparametric method for constructing taper equation. The generalized additive taper equation based on BS spline has the highest prediction accuracy. It’s suitable for the prediction of the shape of Scots pine.